The amount of data processed and stored in the cloud is growing dramatically. The traditional storage devices at both hardware and software levels cannot meet the requirement of the cloud. This fact motivates the need for a plat¬form which can handle this problem. Hadoop is a deployed platform proposed to overcome this big data problem which often uses MapReduce architecture to process vast amounts of data of the cloud system. Hadoop has no strategy to assure the safety and confidentiality of the files saved inside the Hadoop distributed File system (HDFS). In the cloud, the protection of sensitive data is a critical issue in which data encryption schemes plays avital rule. This research proposes a hybrid system between two well-known asymmetric key cryptosystems (RSA, and Paillier) to encrypt the files stored in HDFS. Thus before saving data in HDFS, the proposed cryptosystem is utilized for encrypting the data. Each user of the cloud might upload files in two ways, non-safe or secure. The hybrid system shows higher computational complexity and less latency in comparison to the RSA cryptosystem alone. 

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